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(20 Feb 2013) Key: citeulike:12060503
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We consider symmetric tensors of format $3 × 3 × 3$ over the prime fields $\mathbbF_2$ and $\mathbbF_3$, and compute their equivalence classes under the action of the direct product of general linear groups. We use computer algebra to determine the set of tensors of each symmetric rank, then we compute the orbit of the group action. We determine the maximum symmetric rank of these tensors over $\mathbbF_2$ and $\mathbbF_3$.
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